Spectrofluorimetric measurements on single-walled carbon nanotubes (SWNTs) isolated in aqueous surfactant suspensions have revealed distinct electronic absorption and emission transitions for more than 30 different semiconducting nanotube species. By combining these fluorimetric results with resonance Raman data, each optical transition has been mapped to a specific (n,m) nanotube structure. Optical spectroscopy can thereby be used to rapidly determine the detailed composition of bulk SWNT samples, providing distributions in both tube diameter and chiral angle. The measured transition frequencies differ substantially from simple theoretical predictions. These deviations may reflect combinations of trigonal warping and excitonic effects.